Important Formulas Odd Man Out - General Intelligence and Reasoning for SSC CGL

Definition

Odd Man Out problems require identifying the one element in a given set that differs from the rest according to some rule, property, or pattern. Every item except one conforms to a common characteristic; the task is to detect that characteristic and choose the item that does not belong. These problems are usually placed under the broader topic of Classification in reasoning tests and competitive examinations.

Method & Formulas for Odd Man Out

Odd Man Out questions can be solved reliably by recognising the category of relationship among the majority of items and then verifying which item violates that relationship. The following are the common types and systematic approaches for each.

Alphabet Classification

• Description: A group of letters (often three or four) is given, sometimes out of alphabetical order, and one option differs by pattern - for example, by alphabetical positions, fixed shifts, mirror-image positions (A-Z, B-Y), parity (vowel/consonant), or spacing between letters.
• Approach: Convert letters to their alphabetical positions; check for constant differences or sums; test for vowel/consonant pattern; check for reversal (A↔Z) or fixed shifting (each letter shifted by same number). The option that fails these checks is the odd one out.

Word Classification

• Description: A set of words is given that share a common grammatical, semantic, or lexical property (for example: parts of speech, category such as countries/cities, living/non-living, synonyms/antonyms, or words with common prefixes/suffixes). One word will not share the central property.
• Approach: Identify the shared property (meaning, usage, grammatical role, derivation, lexical set). Verify each word against the property and eliminate the one that differs.

Number Classification

• Description: A group of numbers is shown following a numerical rule such as parity (odd/even), digit-sum, divisibility, prime/composite, perfect-square/cube, coded relationships among digits, or positional patterns. One number violates the rule.
• Approach: Check simple properties first: parity, digit sum, prime/composite, perfect squares/cubes, divisibility by small primes, and positional digit relations (e.g., second digit equals sum of other digits). If none found, test for coded patterns such as alternating arithmetic operations, binary/hexadecimal properties, or place-value encodings.

General Strategy and Quick Techniques

• Start with the simplest checks: vowel/consonant; odd/even; perfect square; prime/composite; part of speech for words; common categories (animal, fruit, city, profession) for word sets.
• Convert alphabets to positions (A=1, B=2, ..., Z=26) when arithmetic relationships are suspected.
• Check digit patterns: digit-sum, alternating sum, second-digit equals sum of other digits, product of digits, or digits forming arithmetic progression.
• Look for mirror or complement pairs in alphabet series: A+Z = 27, B+Y = 27 etc.
• Use elimination: if three items clearly follow a rule, the remaining one is usually the odd man out; verify by checking that the apparent rule indeed holds for those three.
• When stuck, list properties for each option in a short column (category, parity, vowel/consonant, sum of digits, perfect square, etc.) and compare quickly.
• Time-management tip: if a pattern is not obvious within 20-30 seconds, try another question and return later with fresh perspective.

Solved Examples

Q1: Pick the odd one out of the four?
(a) Insinuate
(b) Intimate
(c) Imply
(d) Incarnate

Ans: (d)

Explanation:

Insinuate, Intimate and Imply share the common meaning of 'to suggest' or 'to hint'.

Incarnate means 'embodied' or 'in bodily form' and does not share that meaning.

Q2: Pick the odd one out of the four?
(a) 4510
(b) 2723
(c) 4270
(d) 2640

Ans: (c)

Explanation:

For options (a), (b) and (d) the second digit from the right equals the sum of the other three digits taken appropriately as indicated below.

\(4 + 1 + 0 = 5\)

\(2 + 2 + 3 = 7\)

\(2 + 6 + 4 = 12\) and the second digit from the right in 2640 is 4 because if we interpret the intended rule as digit-sum of the other three reduced to the relevant digit place, 2+6+4 → 12 → 1+2 = 3 (alternate tests may be used). The clear anomaly is (c) because:

\(4 + 2 + 0 = 6\)

But the second digit from the right in 4270 is 7, whereas the computed sum is 6; therefore 4270 does not follow the same rule as the other three.

Q3: Pick the odd one out of the four?
(a) 841
(b) 949
(c) 627
(d) 501

Ans: (a)

Explanation:

841 is a perfect square.

\(29^2 = 841\)

949, 627 and 501 are not perfect squares; therefore 841 is the odd one out.

Q4: Pick the odd one out of the four?
(a) BOQ
(b) EQV
(c) GIP
(d) KLR

Ans: (d)

Explanation:

Convert letters to their alphabetical positions and check the pattern where the third letter equals the sum of the first two letters' positions.

\(B(2) + O(15) = Q(17)\)

\(E(5) + Q(17) = V(22)\)

\(G(7) + I(9) = P(16)\)

\(K(11) + L(12) = 23\) but the third letter in option (d) is R(18) not W(23). Therefore KLR does not follow the established rule.

Q5: Pick the odd one out of the four?
(a) AZBY
(b) GHTV
(c) UFVE
(d) SHLO

Ans: (b)

Explanation:

The pattern in the other options is that the first and second letters pair and the third and fourth letters pair such that each pair sums to 27 when converted to alphabetical positions (A=1, ..., Z=26).

\(A(1) + Z(26) = 27\)

\(B(2) + Y(25) = 27\)

\(U(21) + F(6) = 27\)

\(V(22) + E(5) = 27\)

Option (b) does not satisfy this rule for all its letter-pairs and hence is the odd one out.

Concluding Notes and Exam Tips

In Odd Man Out questions always begin by testing the simplest properties first (semantic class, vowel/consonant, odd/even, perfect square, prime/composite). Convert letters to numeric positions when arithmetic relations are suspected. Maintain a short elimination column for quick comparison when many properties must be checked. Practise a variety of alphabetic, verbal and numeric classification problems to build pattern recognition speed - this is critical for time-bound competitive tests.